Being of European Citizenship - can I buy a US sailboat and take it down to Mexico ?

I am of swiss origin and I am living down in Puerto Vallarta - Mexico.

Thinking of buying a sailboat to cruise the famous Bahia de Banderas
I have been looking at a lot of boats on sale down here lately.

But it is just hairrising what the prices are for boats that I would not
even like to take out of the harbour ...

So I found myself a lot better source ... ebay ... I am thinking of buying
myself a boat in California - sail it down here - and take it maybe even
back home with me to Europe afterwards ... doing a half-circumnavigation.

Does anybody know whether it is a problem for me beeing of a European
Country to actually buy a US registered vessel ?